A.20 Fisher’s z distribution
X has a z distribution on 
and 
degrees of freedom, denoted
if 
, or equivalently if it has the density
Another definition is that if 
, then
The mean and variance are easily deduced from those of the log chi-squared distribution; they are
where 
is (as above) the digamma function, or approximately
The mode is zero.
Unless 
and are very small, the distribution of z is ...
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